3. If is measured in radian Then: If is measured in radian Then: and: - <1-cos < - < sin <

4. From the theorem, and by sandwich theorem, We find that a) - < < 0 0 0As sin= 0

5. And b)- < 1-cos <so 0 0 0 As 1-cos =0 Cos = 1

6. Example Find the limit if it exists:

7. Example g(  )=1 h(  )= cos 

8. Example & therefore…

9. If we graph, it appears that

10. Find the following limits: a) Put = 3x so as x 0, = 3x 0 1 = = Solution

11. b) = = = Solution

12. Put = sin x so as x 0, = sin x 0 = Find ==1 Solution

13. Find: = = = = = = Solution

14. 1) Find = Put = t- so as t, 0. = 1 = Solution

15. Derivative of y = sin x WHY?

16. = 0 +cos(x)*1 = cos (x)

17. Derivative of Sine, Cosine

18. Examples: f(x) = x 2 +sin(x) f’(x) = 2x + cos(x) f(t) = cos(t) – 5t -2, then f '(t) = -sin (t) +10t -3 Derivative of Sine, Cosine

19. Find tan x tan x = = = Solution

20. Derivatives of Trigonometric Functions

21. Find if : 1) Y= Solution

22. 2) Y = Find y’ if y = Solution

24. Find: = ==

25. Has a tangent at x = 0. Show that the function : F(x) = X 0 X = 0

26. Find the values of a and b s.t the function : F(x) =, x 2, x < 2 Is diff. Every where.